This gives the average time starting from \(j\)  and conditioned on hitting the target \(i\) . Similar expressions can be obtained for the ever-return probability \({\cal P}_{ii}\)  and mean first-return time \(\langle t_{ii}\rangle \)  [1]}. These expressions simplify in the downward approximation. To zeroth order in this approximation, the network becomes
acyclic, and therefore \(\left({1} - T(s)\right)^{-1}_{ii} \simeq 1\) . It follows that
\({\cal P}_{ij} \simeq \left({1} - T\right)^{-1}_{ij} \qquad (i\ne j)\,.\) 
